To deal with it in more detail:

Step two. Create two isoceles triangles, one giving the angular distance of the Sun in the sky, one giving the angular distance of the moon. We can fill in these values.

We want the angles to be equal, to give the situation of a total eclipse. The angular distance of both objects will be the same. So in both triangles, the angle will be x. The side opposite this angle will have length M (the apparent size of the moon) in the moon triangle, and 1.3 M in the Sun triangle.

This makes no sense at all.

What you are actually doing here is merely making the sun 1.3 times the distance to the moon, and 1.3 times the size of the moon.

What you actually need to do is have 2 angles, one will be x, the angular size of the moon, and the other will be p x, the angular size of the sun.

This ratio is a ratio of the angles, not a ratio of the sizes of the lines.

The sizes of the lines can be 2M, the diameter of the moon and 2S, the diameter of the sun.

We can also break it into 2 simple right angle triangles rather than 2 isosceles triangles which massively simplifies the math (but means we use x/2 and p x/2 for the angles)

I cannot write math into the forum

So you know it's full of shit and are trying to hide it?

but I expect any capable reader will be able to run through and verify the calculations for themselves.

They sure as hell can verify that what you are saying is pure nonsense.

You don't even need to be good at math to realise what you are saying is crap.

You are trying to determine the distance between 2 objects to give them a ratio of angular size, with no indication of the size of either object (or their relative size).

You will find that the distance to the moon, k+c, is k/p times the square root of (2-p^{2})

But just to check the math, doing what you actually asked for, where you have the moon and the sun being the same angular size (x), with the sun having a diameter p times that of the moon (which itself is M), where the distance along the diagonal to the moon is c, and to the sun is c+k, using the cosine rule (c^2=a^2+b^2-2*a*b*cos(C), which for an isosceles triangle can be simplified to c^2=a^2+a^2-2*a*acos(C)=2*a^2-2*a^2*cos(C)=2*a^2*(1-cos(C), which can be further simplified to c=2*a*sqrt(1-cos(C))

For the moon we get the equation:

M=2*c*sqrt(1-cos(x))

Which can be rearranged to give:

sqrt(1-cos(x))=M/2c

For the sun we get the equation:

p*M=2*(c+k)*sqrt(1-cos(x))

Subbing in the rearranged equation from the moon we get:

p*M=2*(c+k)*M/2c

Which is simplified to:

p=(c+k)/c

and rearranged to:

c+k=c p

Thus the distance to the sun (c+k), is simply c times p, which you could have easily gotten via rules regarding similar triangles.

But notice how this doesn't match your math?

So even with all the prior false claims, you are still wrong here again.

Doing it properly, where you note the sun is roughly 400 times the size of the moon, this means the sun needs to be roughly 400 times further away. So using the approximate distance of 150 million km to the sun, this would put the moon 375 000 km from Earth.

Certainly, there is some error in this calculation.

Well that is one thing you got right. There is so much error it isn't funny. As some would say "it isn't even wrong."

The RE values are dramatically far from what it is RET states.

No, it is dramatically different from what you state, which is nothing like what RET nor HC theory state.

**Edit**: Breakdown to demonstrate how many of the responses are either evasion or misunderstanding.

Your entire OP seems to be misunderstanding and evasion.

Their relative sizes stay the same during an annular eclipse. Only the distances change.

Yes, their relative sizes remain the same, with the sun remaining roughly 400 times the size of the moon.

Notice how 400 is nothing like your 1.3?

None of this relies on any assumptions, beyond the basic assumptions of math and logic. It applies to both FET and RET, but if we apply it to the RE numbers, they fail.

You mean except discarding basic math and logic.

And that's me signing off. Forty posts and everything can be responded to with the OP. Round earthers and all their usual ignorance and total lack of understanding.

Not that any of you are ever going to admit anything. The fact you repeat your bullshit for this long is something you'll take as a victory, I've seen it. Oh, the thread went on over a page, that dumb FEer must have been refuted in that time. It's not like all REers do is repeat the same handful of things and whine like a baby whenever anything goes past that. It's not like you always rely on bullshit.

I win. Again. Goodbye.

You mean that's you running away because you have been refuted yet again.

You are the one displaying ignorance and a total lack of understand. You lose yet again.